/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 State the period of each functio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 12

State the period of each function. $$y=\csc \frac{x}{2}$$

Short Answer

Expert verified
The period of the function \(y=\csc \frac{x}{2}\) is \(4 \pi\).

Step by step solution

01

Recall the Base Function Period

Remember that the base cosecant function, \(y = \csc x\), has a period of \(2 \pi\). This is a vital part of this problem.
02

Identify the Modified Function

Here, \(x\) is divided by \(2\), producing \(y=\csc \frac{x}{2}\). This changes the period. Whenever we have \(y=\csc kx\), where \(k\) is a constant, the period is changed from \(2 \pi\) to \( \frac{2 \pi}{|k|}\).
03

Calculate the Period of the given Function

So, for this function, \( \frac{x}{2}\) in the Cosecant function changes the period to \(\frac{2 \pi}{\left|\frac{1}{2}\right|}\) which simplifies to \(4 \pi\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The average high temperature \(T,\) in degrees Fahrenheit, for Fairbanks, Alaska, is given by $$ T(t)=-41 \cos \left(\frac{\pi}{6} t\right)+36 $$ where \(t\) is the number of months after January \(5 .\) Use the formula to estimate (to the nearest 0.1 degree Fahrenheit) the average high temperature in Fairbanks for March 5 and July 20.

Graph at least one full period of the function defined by each equation. $$y=\left|-\frac{1}{2} \cos \frac{x}{2}\right|$$

Simplify: \(\frac{2 \pi}{1 / 3}\).

Use a graphing utility to graph each function. $$y=\cos |x|$$

Graph at least one full period of the function defined by each equation. $$y=2 \cos 2 x$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.